3,634 research outputs found
The Solar-Interior Equation of State with the Path-Integral Formalism I. Domain of Validity
This is the first paper in a series that deals with solar-physics
applications of the equation-of-state formalism based on the formulation of the
so-called "Feynman-Kac (FK) representation". Here, the FK equation of state is
presented and adapted for solar applications. Its domain of validity is
assessed. The practical application to the Sun will be dealt with in Paper II.
Paper III will extend the current FK formalism to a higher order. Use of the FK
equation of state is limited to physical conditions for which more than 90% of
helium is ionized. This incudes the inner region of the Sun out to about .98 of
the solar radius. Despite this limitation, in the parts of the Sun where it is
applicable, the FK equation of state has the power to be more accurate than the
equations of state currently used in solar modeling. The FK approach is
especially suited to study physical effects such as Coulomb screening, bound
states, the onset of recombination of fully ionized species, as well as
diffraction and exchange effects. The localizing power of helioseismology
allows a test of the FK equation of state. Such a test will be beneficial both
for better solar models and for tighter solar constraints of the equation of
state.Comment: Completely rewritten revised version. Accepted for publication in
Astronomy & Astrophysic
Analysis and Hermite spectral approximation of diffusive-viscous wave equations in unbounded domains arising in geophysics
The diffusive-viscous wave equation (DVWE) is widely used in seismic
exploration since it can explain frequency-dependent seismic reflections in a
reservoir with hydrocarbons. Most of the existing numerical approximations for
the DVWE are based on domain truncation with ad hoc boundary conditions.
However, this would generate artificial reflections as well as truncation
errors. To this end, we directly consider the DVWE in unbounded domains. We
first show the existence, uniqueness, and regularity of the solution of the
DVWE. We then develop a Hermite spectral Galerkin scheme and derive the
corresponding error estimate showing that the Hermite spectral Galerkin
approximation delivers a spectral rate of convergence provided sufficiently
smooth solutions. Several numerical experiments with constant and discontinuous
coefficients are provided to verify the theoretical result and to demonstrate
the effectiveness of the proposed method. In particular, We verify the error
estimate for both smooth and non-smooth source terms and initial conditions. In
view of the error estimate and the regularity result, we show the sharpness of
the convergence rate in terms of the regularity of the source term. We also
show that the artificial reflection does not occur by using the present method.Comment: 32 pages, 27 figure
Diamagnetic response and phase stiffness for interacting isolated narrow bands
A platform that serves as an ideal playground for realizing ``high''
temperature superconductors are materials where the electrons' kinetic energy
is completely quenched, and interactions provide the only energy scale in the
problem for . However, when the non-interacting bandwidth for a set of
isolated bands is small compared to the scale of the interactions, the problem
is inherently non-perturbative and requires going beyond the traditional
mean-field theory of superconductivity. In two spatial dimensions, is
controlled by the superconducting phase stiffness. Here we present a general
theoretical framework for computing the electromagnetic response for generic
model Hamiltonians, which controls the maximum possible superconducting phase
stiffness and thereby , without resorting to any mean-field approximation.
Importantly, our explicit computations demonstrate that the contribution to the
phase stiffness arises from (i) ``integrating out'' the remote bands that
couple to the microscopic current operator, and (ii) the density-density
interactions projected onto the isolated narrow bands. Our framework can be
used to obtain an upper bound on the phase stiffness, and relatedly the
superconducting transition temperature, for a range of physically inspired
models involving both topological and non-topological narrow bands with
arbitrary density-density interactions. We discuss a number of salient aspects
of this formalism by applying it to a specific model of interacting flat bands
and compare it against the known from independent numerically exact
computations.Comment: 7 + 4 pages, 3 figures, new results adde
The Mason Test: A Defense Against Sybil Attacks in Wireless Networks Without Trusted Authorities
Wireless networks are vulnerable to Sybil attacks, in which a malicious node
poses as many identities in order to gain disproportionate influence. Many
defenses based on spatial variability of wireless channels exist, but depend
either on detailed, multi-tap channel estimation - something not exposed on
commodity 802.11 devices - or valid RSSI observations from multiple trusted
sources, e.g., corporate access points - something not directly available in ad
hoc and delay-tolerant networks with potentially malicious neighbors. We extend
these techniques to be practical for wireless ad hoc networks of commodity
802.11 devices. Specifically, we propose two efficient methods for separating
the valid RSSI observations of behaving nodes from those falsified by malicious
participants. Further, we note that prior signalprint methods are easily
defeated by mobile attackers and develop an appropriate challenge-response
defense. Finally, we present the Mason test, the first implementation of these
techniques for ad hoc and delay-tolerant networks of commodity 802.11 devices.
We illustrate its performance in several real-world scenarios
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